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894
Symbolic Model Checking: 10^20 States and Beyond
, 1992
"... Many different methods have been devised for automatically verifying finite state systems by examining stategraph models of system behavior. These methods all depend on decision procedures that explicitly represent the state space using a list or a table that grows in proportion to the number of st ..."
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Cited by 758 (41 self)
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, strong and weak observational equivalence of finite transition systems, and language containment for finite wautomata. The fixed point computations for each decision procedure are sometimes complex. but can be concisely expressed in the MuCalculus. We illustrate the practicality of our approach
A calculus of mobile processes, I
, 1992
"... We present the acalculus, a calculus of communicating systems in which one can naturally express processes which have changing structure. Not only may the component agents of a system be arbitrarily linked, but a communication between neighbours may carry information which changes that linkage. The ..."
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Cited by 1184 (31 self)
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calculus of higherorder functions (the Icalculus and combinatory algebra), the transmission of processes as values, and the representation of data structures as processes. The paper continues by presenting the algebraic theory of strong bisimilarity and strong equivalence, including a new notion of equivalence
Weak Equivalences in Psicalculi
"... Psicalculi extend the picalculus with nominal datatypes to represent data, communication channels, and logics for facts and conditions. This general framework admits highly expressive formalisms such as concurrent higherorder constraints and advanced cryptographic primitives. We here establish th ..."
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Cited by 10 (5 self)
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demonstrate that the complications mainly stem from psicalculi where the associated logic does not satisfy weakening. We prove that weak bisimulation equivalence has the expected algebraic properties and that the corresponding observation congruence is preserved by all operators. These proofs have been
TENSOR RANK AND THE ILLPOSEDNESS OF THE BEST LOWRANK APPROXIMATION PROBLEM
"... There has been continued interest in seeking a theorem describing optimal lowrank approximations to tensors of order 3 or higher, that parallels the Eckart–Young theorem for matrices. In this paper, we argue that the naive approach to this problem is doomed to failure because, unlike matrices, te ..."
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Cited by 194 (13 self)
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and order2 tensors (i.e. matrices). In a more positive spirit, we propose a natural way of overcoming the illposedness of the lowrank approximation problem, by using weak solutions when true solutions do not exist. For this to work, it is necessary to characterize the set of weak solutions, and we do
Weaknesses of Margulis and RamanujanMargulis LowDensity ParityCheck Codes
 Electronic Notes in Theoretical Computer Science
, 2003
"... We report weaknesses in two algebraic constructions of lowdensity paritycheck codes based on expander graphs. The Margulis construction gives a code with nearcodewords, which cause problems for the sumproduct decoder; The RamanujanMargulis construction gives a code with lowweight codewords, whic ..."
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Cited by 90 (1 self)
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We report weaknesses in two algebraic constructions of lowdensity paritycheck codes based on expander graphs. The Margulis construction gives a code with nearcodewords, which cause problems for the sumproduct decoder; The RamanujanMargulis construction gives a code with lowweight codewords
The ASTOOT approach to testing objectoriented programs
 ACM Transactions on Software Engineering
, 1994
"... This article describes a new approach to the unit testing of objectoriented programs, a set of tools based on this approach, and two case studies. In this approach, each test case consists of a tuple of sequences of messages, along with tags indicating whether these sequences should put objects of ..."
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Cited by 182 (1 self)
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of the class under test into equivalent states and\or return objects that are in equivalent states. Tests are executed by sending the sequences to objects of the class under test, then invoking a usersupplied equivalencechecking mechanism. This approach allows for substantial automation of many aspects
Coil sensitivity encoding for fast MRI. In:
 Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
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Cited by 193 (3 self)
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reconstruction from multiple receiver data. Using the framework of linear algebra, two different reconstruction strategies have been derived. In their general forms the resulting formulae hold for arbitrary sampling patterns in kspace. A detailed discussion is dedicated to the most practical case, namely
From subfactors to categories and topology I. Frobenius algebras in and Morita equivalence of tensor categories
 J. Pure Appl. Alg
, 2003
"... We consider certain categorical structures that are implicit in subfactor theory. Making the connection between subfactor theory (at finite index) and category theory explicit sheds light on both subjects. Furthermore, it allows various generalizations of these structures, e.g. to arbitrary ground f ..."
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Cited by 103 (9 self)
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to the bicategory E. We define weak monoidal Morita equivalence of tensor categories, denoted A ≈ B, and establish a correspondence between Frobenius algebras in A and tensor categories B ≈ A. While considerably weaker than equivalence of tensor categories, weak monoidal Morita equivalence A ≈ B has remarkable
Weakly Equivalent Arrays
"... The (extensional) theory of arrays is widely used to model systems. Hence, efficient decision procedures are needed to model check such systems. Current decision procedures for the theory of arrays saturate the readoverwrite and extensionality axioms originally proposed by McCarthy. Various filte ..."
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filters are used to limit the number of axiom instantiations while preserving completeness. We present an algorithm that lazily instantiates lemmas based on weak equivalence classes. These lemmas are easier to interpolate as they only contain existing terms. We formally define weak equivalence and show
On weak Lie 2algebras
"... Abstract. A Lie 2algebra is a linear category equipped with a functorial bilinear operation satisfying skewsymmetry and Jacobi identity up to natural transformations which themselves obey coherence laws of their own. Functors and natural transformations between Lie 2algebras can also be defined, ..."
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Cited by 24 (0 self)
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, yielding a 2category. Passing to the normalized chain complex gives an equivalence of 2categories between Lie 2algebras and certain “up to homotopy " structures on the complex; for strictly skewsymmetric Lie 2algebras these are L∞algebras, by a result of Baez and Crans. Lie 2algebras appear
Results 1  10
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894